相关论文: Quantum Field Symbolic Analog Computation: Relativ…
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks and neuromorphic computing. Further important examples are cellular automata and differential analyzers.…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing…
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge…
Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and conceptual levels. It is related to quantum…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…